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Article Dans Une Revue Theoretical Computer Science Année : 2015

Real or natural numbers interpretations and their effect on complexity

Antoine Henrot
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Résumé

Interpretation methods have been introduced in the 70’s by Lankford in rewriting theory to prove termination. Actually, as shown by Bonfante et al., they provide some good tools to prove the complexity of programs. However, such an analysis depends deeply on the archimedean property of natural numbers. This is in contradiction with the fact that finding an interpretation can be solved by Tarski’s decision procedure (as described by Dershowitz), and consequently interpretations are usually chosen over the reals rather than over the integers. Doing so, one cannot use anymore the (good) properties of the natural (welordering of N used to bound the complexity of programs. We prove that one may benefit from the best of both worlds: the complexity analysis still holds even with real numbers. The reason lies in a deep algebraic property of polynomials over the reals. We illustrate this by two characterizations, one of polynomial time and one of polynomial space.

Dates et versions

hal-01093579 , version 1 (10-12-2014)

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Guillaume Bonfante, Florian Deloup, Antoine Henrot. Real or natural numbers interpretations and their effect on complexity. Theoretical Computer Science, 2015, 585, pp.25-40. ⟨10.1016/j.tcs.2015.03.004⟩. ⟨hal-01093579⟩
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